中文摘要：

对于一个具有n-进位吸引子的区间连续映射，证明了：“n不是2的方幂”是该映射具有正拓扑熵的充分条件但不是必要条件；探讨了函数方程f^3（λx）=λf（x）的一类解，并证明这类解中的每一个成员都有3-进位吸引子．

英文摘要：

The notion of adic attractor is introduced. For a continuous interval map with nadic attractor, the paper proves that the condition that n is not a power of 2 is sufficient but not necessary for the map to have positive topological entropy. And a class of solutions of the functional equation f^3（λx） = λf（x）, which will be proved to have 3-adic attractor, are investigated.